Calculating the Bending Moment of a Steel Tube

In summary, the user is seeking help with calculating the bending moment of a steel tube with specific dimensions. They mention needing to use Young's modulus and ask for the correct formula. In response, the expert clarifies that the support conditions of the tube are important in determining the bending moments and explains the process of analyzing the cross section for maximum moments. They also mention the stress relationship \sigma=\frac{My}{I} and ask if the user is looking for the yield criteria.
  • #1
fcukniles
26
0
Hi,
I need to work out the bending moment of a steel tube, 25mm diameter (3mm thick) 410mm long.

im assuming i have to use youngs modulus in some way? what's the correct formula for working out when it will bend?
thanks
chris
 
Physics news on Phys.org
  • #2
fcukniles said:
Hi,
I need to work out the bending moment of a steel tube, 25mm diameter (3mm thick) 410mm long.

im assuming i have to use youngs modulus in some way? what's the correct formula for working out when it will bend?
thanks
chris

How is the tube supported? This is a very important detail when determing bending moments. Cantalevered beams will have different support reactions than simply supported beams... Essentially what you need to do is determine the support reactions on the tube as if it were solid; additionally, you need to find the point of maximum moment along the tube (this is where the support conditions come into play). Once you know where along the tube the max/min moments are to be found you can then draw a 3D FBD of the cross section and analyze how bending effects the top and bottom(or wherever the max moments may be) differential cross sectional areas of the tube.

See attached picture. The red bar is the tub modeled as a solid and the blue/white pipe is a section of the tube at the point of max moment(under the force in this case). There is a stress relationship [itex]\sigma=\frac{My}{I}[/itex] where M is the moment, y is the distance from the centroid to the point of concern(usually point of maximum stress which occurs at the outer edge of the cross section) and I is the moment of inertia.

Is that what you were looking for?

[edit]The pipe will always bend no matter how much or little it is loaded unless it is supported along a free surface i.e. resting on a flat smooth surface. Are you looking for the yield criteria (max moment just before the onset of permanate plastic deformation)?
 

Attachments

  • bending_moment.PNG
    bending_moment.PNG
    5.4 KB · Views: 590
Last edited:
  • #3


Hi Chris,

To calculate the bending moment of a steel tube, you can use the formula M = F * d, where M is the bending moment, F is the force applied, and d is the distance from the point of rotation to the force.

In this case, the force is the weight of the tube itself, and the distance from the point of rotation (the center of the tube) to the force can be calculated as half of the length of the tube (205mm).

Now, to determine the force, you need to calculate the weight of the tube. This can be done using the formula W = m * g, where W is the weight, m is the mass, and g is the gravitational acceleration (9.8 m/s^2).

The mass of the tube can be calculated by multiplying its volume (pi * r^2 * h) by its density. As the tube is 25mm in diameter and 410mm long, its volume would be approximately 15,707 mm^3. The density of steel is around 7,850 kg/m^3, so the mass of the tube would be 0.123 kg.

Plugging these values into the formula, we get W = 0.123 kg * 9.8 m/s^2 = 1.206 N.

Finally, we can calculate the bending moment by multiplying the force by the distance: M = 1.206 N * 205mm = 247.23 N*mm.

As for Young's modulus, it is a measure of a material's stiffness, but it is not necessary to use it in this calculation. It is typically used to determine the deflection of a material under a given load, but in this case, we are only interested in the bending moment.

I hope this helps! Let me know if you have any further questions.
 

What is the formula for calculating the bending moment of a steel tube?

The formula for calculating the bending moment of a steel tube is M = F * d, where M is the bending moment, F is the applied force, and d is the distance from the force to the neutral axis.

How do I determine the appropriate cross-sectional area for a steel tube?

The appropriate cross-sectional area for a steel tube can be determined by considering the maximum bending moment the tube will experience and selecting a tube with a sufficient moment of inertia to resist that force.

What factors affect the bending moment of a steel tube?

The bending moment of a steel tube is affected by several factors including the applied force, the distance from the force to the neutral axis, the cross-sectional area, and the material properties of the steel.

Can the bending moment of a steel tube be reduced?

Yes, the bending moment of a steel tube can be reduced by increasing the distance from the force to the neutral axis, choosing a tube with a larger cross-sectional area, or using a stronger steel material.

How does the bending moment differ between a steel tube and a solid steel bar?

The bending moment of a steel tube and a solid steel bar will differ due to the different cross-sectional areas and moments of inertia. A steel tube will be able to resist a greater bending moment due to its hollow shape and larger moment of inertia compared to a solid steel bar of the same dimensions.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
1K
Replies
3
Views
529
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
271
  • Introductory Physics Homework Help
Replies
8
Views
5K
  • Mechanical Engineering
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Replies
5
Views
4K
  • Mechanical Engineering
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
Back
Top